Question

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients. Are x2-7x+12

Answer 1

Step-by-step explanation:

Given that, zeros the quadratic polynomial is x² + 7x + 12. Since the above equation is in the form ax² + bx + c= 0. So, we can solve it by Quadratic formula or by Splitting the middle term....

HOPE THIS WILL HELP YOU

Answer 2

Given :

• A polynomial x²-7x+12.

To Find :

• Zeroes of the given polynomial and verify relationship between the zeroes and their coefficients.

Solution :

$\longmapsto\tt\bf{{x}^{2}-7x+12}$

By Splitting Middle Term :

$\longmapsto\tt{{x}^{2}-(4x+3x)+12}$

$\longmapsto\tt{{x}^{2}-4x-3x+12}$

$\longmapsto\tt{x(x-4)-3(x-4)}$

$\longmapsto\tt{(x-3)\:(x-4)}$

• x = 3
• x = 4

So , 3 and 4 are the zeroes of polynomial x²-7x+12..

_______________________

Here :

• a = 1
• b = -7
• c = 12

Sum of Zeroes :

$\longmapsto\tt{\alpha+\beta=\dfrac{-b}{a}}$

$\longmapsto\tt{3+4=\dfrac{-(-7)}{1}}$

$\longmapsto\tt\bf{7=7}$

Product of Zeroes :

$\longmapsto\tt{\alpha\beta=\dfrac{c}{a}}$

$\longmapsto\tt{3\times{4}=\dfrac{12}{1}}$

$\longmapsto\tt\bf{12=12}$

HENCE VERIFIED